TY - JOUR T1 - A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's AU - Abe , Kosuke AU - Higashimori , Nobuyuki AU - Kubo , Masayoshi AU - Fujiwara , Hiroshi AU - Iso , Yuusuke JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 693 EP - 698 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2014.5.s6 UR - https://global-sci.org/intro/article_detail/aamm/43.html KW - Numerical analysis, finite difference scheme, stability, CFL condition. AB -

The Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.